Statistical Invent iyntioiut 3H5 



and intolktctually an uiiinturoxting )M)ing, The clans to wliich ho belongn ut bulky aiid no duuhl 

 survtw to help lh« courHeuf Hocial life in action. It aliH> afli>nl8, liy itH inertia, a regulator that, 

 lik« the Hy-wli<-el t<> the dtouuiengine, riwiHU Hudden and irn<guliir changeH. Hut the average 

 man is of no dinvt help towanlH evolution, which app<MirH to our dim viHion to lie the goal of 

 all living existence. Evolution is an unrenting progrewiion ; the nature of the average individual 

 in OHsontially unprogressive. Consider the int«nwt attairlu^d to the Hebrew race, wliose average 

 value iH little worthy of note, but which is of special impijrtHnce on account of itft variety. Its 

 variability in ancient and modern times Hoems to have Ixvn extnionlinarily great. It has been 

 able to supply men, time after time, who have towered high alwve their fellows, and left enduring 

 marks on th(> history of the world. 



Some thoroughgoing denux^rats may look with complacency on a mob of m<<diocritie^ but 

 to most other jH-r.sons the)- are the reverse of attractive. The al)8cnce of heroic gifts among 

 them would be a luwivy set off against the frmnlom from a corres|)onding numln-r of very degraded 

 forms. The general standard of thought and morals in a mob of iii(><li(x:rities must necessarily 

 1)0 mediocre, and, what is worse, cont<!ntedly so. The lack of living men to afTonl lofty examples, 

 and to educate the virtue of reverence, leaves an irremotliable blank. All men would lind them- 

 selves at nearly the same dojid average level, each btiing as mcAnly endowed as his neighbour. 

 These remarks apply with obvious moditioation to variety in the physical faculties. Peculiar 

 gifts, moreover, alibrd an especial justitication for division of labour, each man doing what ho 

 can do best." (pp. 15-16.) 



Coultl any man but Galton have written a sermon like the above to bring 

 out the essential meaning to liumanity of — let us say — the standard deviation 

 or the quartile? Could any man have written thus but Galton without laying 

 himself" o{)en to the charge of self-conceit? He did not regard himself as one 

 whose faculties gave him rank in the extreme tail of a frefjuency distribu- 

 tion. He would have recognised such a position for half his friends, before 

 he thought of it for himself He pictured life statistically, and with the naive- 

 ness of a child spoke the truth, forgetting that he wjis talking to a crowd 

 the bulk of whom must have been sufficiently introspective to doubt whether 

 they were not themselves mediocrities. Perhaps there is little to wonder 

 at, if Galton's words fell on barren ground, and his brother anthropologists 

 have continued for more than thirty years to neglect variation and cultivate 

 mediocrity by ascertaining means. 



Galton in his next section, "The Measurement of Variety," proceeds to 

 describe his method of reaching the median M and the quartile Q from any 

 two sets of observations, i.e. from any two percentiles, thus generalising his 

 previous results, for directly finding M and Q. He suggests that a traveller 

 among savage peoples might test them by finding wnat percentages could 

 stretch two (or better three) bows, the bows having oeen previously tested by 

 the numl)ers of pounds' weight which were required to stretch them to the 

 full'. Similar tests might be easily applied to the delicacy of hearing and eye- 

 sight, to swiftness in running, accuracy of aim, with spear, arrow, sling, etc. 



' Let X, and x^ be the unknown distances from the median ni, of the two known test value^t 

 t^ and /,. Then x^ = x-^ja = (m - <,)/{r and x,' = Xj/o- = {t.t — m)ja, where <r is the standard deviation, 

 can be found at once from the tables of the probability integral, taking as standard case, one 

 percentage above and one below the median (60 °/,). Solving for m and <r we have : 



m = (x,' t^ + X,' ^)/(x,' + X,') and <t = (^ - <,)/(x,' + x,'), 



which solve the problem. Galton works with the quartile instead of a; but assumes the normal 

 relation of the two. 



F o II 40 



